I am right handed and wear mine on the right with my powder horn. This was the way I started doing it and I've never tried anyother way... To me it feels right, and like others have said, I can feel around in it and bring out whatever I would need...
I must admit, I did not know there was a right and left hand bag, I just thought they were all "universal", so I have learned something! 
JOE, I add a short starter/ pistol ram rod loop on the side of my bags between the back panel and gusset, also a buckle on the strap, the buckle is on the shorter end of the strap, if you buy a left handed bag and wear it on the right , the buckle winds up on the front of the and the short strater loop on the back, now you can cut the loop off if desired , the buckle is not a big deal to some people, but to me its in the way and it can possibly scratch the stock on you most precious smokepole! I add the buckle and extra long straps when I make then for adjustment for some of us more rounded out fellas and for adjustment when layering for winter! buy the way Im right handed and wear my pouch on the left.